Correspondence chess is played by long-distance correspondence, through a correspondence chess server, through email or by post. It is possible to build friendships with people with whom you have something in common without actually meeting. Some people like this aspect of it.
The length of a game depends on the mode of communication. Games played electronically would tend to last a few days or maybe a couple of weeks.
Postal chess has a longer history in chess dating back a couple of centuries. Games played by post will take somewhat longer.
Time limits are decided between the players before the games and these vary depending on the circumstances. Mistakes are rarer in postal chess given the greater amount of time available for calculations. So if you mess up it can be difficult to rectify the situation!